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Apr 04, 2019Open AccessArticle
Forecasting of static processes and estimation of random fields of a different nature is becoming more widespread among scientists of different specialties, and a new branch of science appears with its specific methodology. That problems of estimation of the unknown values of random fields are generalization of problems of extrapolation, interpolation and filtering of stochastic processes. The study of the dependence of the obtained formulas on the geometry and the number of embeds are the topic...
Mathematical Analysis
Applied Statistical Mathematics
Algebra
Apr 04, 2019Open AccessArticle
Nowadays, science is characterized by needs of the study of various complex processes and phenomena’s. Today’s research of complex and dynamical systems is one of the most advanced ways of research and evolution of the modern world. Models of biology and ecology, physical models, various economic and social models are typical examples of dynamic systems.
The concept of an interactive complex system in modern science is a main tool for construction of mathematical models for solving modern civil...
Applied Statistical Mathematics
Dynamical System
Algebra
Apr 04, 2019Open AccessArticle
Hidden Markov models are a well-known probabilistic graphical model for time series of discrete, partially observable stochastic processes. We consider the method to extend the application of hidden Markov models to non-Gaussian continuous distributions by embedding a priori probability distribution of the state space into reproducing kernel Hilbert space. Corresponding regularization techniques are proposed to reduce the tendency to overfitting and computational complexity of the algorithm, i.e...
Applied Statistical Mathematics
Algebra
Apr 04, 2019Open AccessArticle
Biotope spaces were introduced by Marchevsky-Steinhaus in for the needs of mathematical biology, namely the study of ecosystems. Biotope distance is defined on the set of all subsets of some finite set X. The distance between any subsets A1 and A2 of X is calculated by the rule: d(A1, A2) = (0, if A1 = A2 = ?; |A1⊕A2| |A1∪A2| , if A1, A2 ∈ B(X)).We introduce a new generalization of a biotope metric to the infinite case using supernatural or Steinitz numbers. A supernatural number (or Steinitz nu...
Applied Statistical Mathematics
Algebraic Geometry
Geometry
Combinatorial Mathematics
Algebra
Feb 09, 2015Open AccessArticle
In this paper, we will see that we can reformulate the purely classical probability theory, using similar language to the one used in quantum mechanics. This leads us to reformulate quantum mechanics itself using this different way of understanding probability theory, which in turn will yield a new interpretation of quantum mechanics. In this reformulation, we still prove the existence of none classical phenomena of quantum mechanics, such as quantum superposition, quantum entanglement, the unce...
Atomic Physics
Particle Physics
Applied Statistical Mathematics
Probability Theory
Modern Physics
Quantum Mechanics
Theoretical Physics
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